Question: Solve for $x$ and $y$ using elimination. ${3x-4y = 3}$ ${-3x-3y = -45}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $-7y = -42$ $\dfrac{-7y}{{-7}} = \dfrac{-42}{{-7}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {3x-4y = 3}\thinspace$ to find $x$ ${3x - 4}{(6)}{= 3}$ $3x-24 = 3$ $3x-24{+24} = 3{+24}$ $3x = 27$ $\dfrac{3x}{{3}} = \dfrac{27}{{3}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {-3x-3y = -45}\thinspace$ and get the same answer for $x$ : ${-3x - 3}{(6)}{= -45}$ ${x = 9}$